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 A354259 Expansion of e.g.f. 1/sqrt(1 - 6 * log(1+x)). 2
 1, 3, 24, 330, 6354, 157482, 4772268, 170950392, 7066790676, 331108863372, 17340063707952, 1003726452207960, 63635982830437320, 4385439331442232840, 326404115258791793040, 26093904013675118381760, 2229931839713559043435920 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Table of n, a(n) for n=0..16. FORMULA E.g.f.: Sum_{k>=0} binomial(2*k,k) * (3 * log(1+x)/2)^k. a(n) = Sum_{k=0..n} (3/2)^k * (2*k)! * Stirling1(n,k)/k!. a(n) ~ n^n / (sqrt(3) * (exp(1/6)-1)^(n + 1/2) * exp(n - 1/12)). - Vaclav Kotesovec, Jun 04 2022 MATHEMATICA With[{nn=20}, CoefficientList[Series[1/Sqrt[1-6Log[1+x]], {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Oct 06 2023 *) PROG (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(1/sqrt(1-6*log(1+x)))) (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, binomial(2*k, k)*(3*log(1+x)/2)^k))) (PARI) a(n) = sum(k=0, n, (3/2)^k*(2*k)!*stirling(n, k, 1)/k!); CROSSREFS Cf. A320343, A354240, A354260. Cf. A354252, A354261. Sequence in context: A232693 A319939 A082166 * A370055 A371007 A144003 Adjacent sequences: A354256 A354257 A354258 * A354260 A354261 A354262 KEYWORD nonn AUTHOR Seiichi Manyama, May 21 2022 STATUS approved

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Last modified June 13 17:32 EDT 2024. Contains 373391 sequences. (Running on oeis4.)